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by: Hyman Bailey

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2

# DiffEquationwithLinearAlg MAT2705

Marketplace > Villanova University > Mathematics (M) > MAT2705 > DiffEquationwithLinearAlg
Hyman Bailey
VU
GPA 3.66

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Hyman Bailey on Wednesday October 28, 2015. The Class Notes belongs to MAT2705 at Villanova University taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/230555/mat2705-villanova-university in Mathematics (M) at Villanova University.

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Date Created: 10/28/15
Modeling USPopulation Growth gt data076 1092 20 106 30 123 40 132 50 151 60 179 70 203 80 2265 90 2487 100 281 These are the population data for the US over the last 100 years E g the pair 076 means that in the year 1900 there were 76 million people living in the US In the year 2000 the census counted 281 million gt plot data stylepoint view0 300 dataplot 3GB 200 39 100 Gllllllllllllll D 25 50 7 5 100 Let s try to match a logistic equation to these data gt logistic t gtL 1Cexp kt 4 1 Cekt To determine the parameters C L and k I plug in the data points for 1960 1980 and 2000 gt sys 179logistic 60 2265logistic80 281logistic100 logistic t gt L sys l79 1 Ce 60k 2265 L 80k 1 Ce L 281 100k 1Ce This system is a bear to solve by hand but it39s no problem for Maple gt solsolvesys CkL sol C 9042375306 k 001567489364 L 8109524047 We substitute these values into our logistic equation gt model subs sol logistic t 8109524047 1 9042375306 6 001567489364t Let s plot this model together with the data points gt with plots gt display dataplot plot model t0 100 colorblue model 300 ff 200 2 f Ulllllllllllllilllllll U 25 50 75 1039 Great t So what will the US population be in 2050 if we believe our model 4357 million gt evalf subs t150 model 4356913502 when does the US population reach the 300 million gt fsolve model300 t 1065033016 answer half way through the year 2006 so just passed

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